Multiscale telescopic imaging system

ABSTRACT

A multiscale telescopic imaging system is disclosed. The system includes an objective lens, having a wide field of view, which forms an intermediate image of a scene at a substantially spherical image surface. A plurality of microcameras in a microcamera array relay image portions of the intermediate image onto their respective focal-plane arrays, while simultaneously correcting at least one localized aberration in their respective image portions. The microcameras in the microcamera array are arranged such that the fields of view of adjacent microcameras overlap enabling field points of the intermediate image to be relayed by multiple microcameras. The microcamera array and objective lens are arranged such that light from the scene can reach the objective lens while mitigating deleterious effects such as obscuration and vignetting.

CROSS REFERENCE TO RELATED APPLICATIONS

This case is a continuation-in-part of co-pending U.S. patentapplication Ser. No. 13/889,007, filed May 7, 2013 (Attorney Docket:525-004US2), which is a continuation-in-part of U.S. patent applicationSer. No. 13/095,407 (Attorney Docket: 525-004US) filed Apr. 27, 2011,which is a continuation-in-part of U.S. patent application Ser. No.12/651,894 (now U.S. Pat. No. 8,259,212), filed 4 Jan. 2010 (AttorneyDocket: 524-005US), which claims priority of U.S. Provisional PatentApplication 61/142,499, filed Jan. 5, 2009 (Attorney Docket: 524-002US),each of which is incorporated herein by reference.

This application also claims priority of provisional patent applicationsU.S. Ser. No. 61/720,469, filed Oct. 31, 2012 (Attorney Docket:DU4043PROV) and U.S. Ser. No. 61/774,910, filed Mar. 8, 2013 (AttorneyDocket: DU4043PROV-2), each of which is incorporated herein byreference.

STATEMENT REGARDING FEDERALLY-SPONSORED RESEARCH

This invention was made with Government support under HR-0011-10C-0073awarded by the Defense Advanced Research Projects Agency (DARPA). TheGovernment has certain rights in the invention.

If there are any contradictions or inconsistencies in language betweenthis application and one or more of the cases that have beenincorporated by reference that might affect the interpretation of theclaims in this case, the claims in this case should be interpreted to beconsistent with the language in this case.

FIELD OF THE INVENTION

The present invention relates to imaging optics in general, and, moreparticularly, to wide field of view imaging systems.

BACKGROUND OF THE INVENTION

Telescopic imaging systems are widely used for imaging scenes throughthe Earth's atmosphere—ground-based telescopes for astronomicalobservation and space-based telescopes for aerial surveillance ofregions of the Earth's surface. The goal of a typical telescopic imagingsystem, such as an astronomical telescope, is to achieve an imageresolution at the limit permissible by scintillation while imaging thelargest solid angle permissible by atmospheric seeing considerations.

A conventional telescopic imaging system includes a long-focal-lengthobjective lens or mirror and a short-focal-length relay lens (i.e.,eyepiece). Over time, successively larger aperture telescopes have beendeveloped to improve telescope performance.

Unfortunately, turbulent mixing (caused by effects such as differenttemperature layers, wind speeds, etc.) can perturb the opticalrefractive index of the Earth's atmosphere. As a result, as light wavestravel through the atmosphere, they can become distorted, leading toimage distortions (e.g., aberrations, speckle, etc.) that manifest asoptical effects like the blurring and twinkling of stars when viewedfrom the Earths' surface. They can also lead to impaired imageresolution for space-based imaging systems used for aerial surveillance.

Atmospheric perturbation is quantified by the diameter of the “seeingdisc,” which is a measure of how severely atmospheric perturbationaffects imaging capability. The seeing disc corresponds to the diameterof a blurred image that results from observation of a point-sourceobject through the atmosphere. Theoretically, the seeing limit throughthe Earth's atmosphere is of order 1 arcsecond (˜0.4 arcseconds has beenachieved at high-altitude observatories on small islands such as MaunaKea or La Palma) without the inclusion of expensive adaptive opticsapproaches to actively correct for aberrations.

The diameter of the objective lens determines the aperture of theimaging system, which, in turn, determines the brightness and sharpnesswith which a telescope can image a scene. Image detail (i.e.,resolution) and the amount of light captured scale with objective-lensaperture. In other words, telescopic imaging systems having largerapertures enable more image detail and fainter objects to be observed.Unfortunately, a larger aperture lens also results in a largerdifference in the optical path of light that travels through the lens onthe optical axis from the optical path of light that travels through thelens off the optical axis. Larger aperture lenses, therefore, inducegreater aberrations on the light passing them. As a result, complexsystem designs that include adaptive optics, speckle masking, additionaloptical surfaces, and/or other atmospheric distortion compensation, arerequired to achieve diffraction-limited performance making larger suchsystems more expensive to fabricate.

It is known that restricting the field of view of a large-aperturetelescope can provide lower-aberration performance, however. Such anapproach has been taken with several such systems that are in operationaround the world, such as the 2.5-meter (m) telescope located at ApachePoint Observatory, New Mexico. This telescope, used in the Sloan DigitalSky Survey, is equipped with a 120-megapixel camera and, althoughconsidered a “wide-field” telescope, has an instantaneous field of viewthat is limited to approximately 1.5 square degrees of sky. As a result,while this telescope can capture multi-color images of over one-quarterof the sky, these images are obtained over an extremely long period oftime due, in part, to the fact that its instantaneous field of view isapproximately equal to about eight times the diameter of the full moon.In similar fashion, the “wide-field,” high-resolution ARGUS-IStelescope, includes a restricted instantaneous field of view ofapproximately 5 arcseconds and a total 45° field of view.

Unfortunately, such prior-art telescopic imaging systems cannot providehigh-resolution images over a large instantaneous field of view. Thisleads to large regions of a scene being unobserved at any given time. Asa result, transient events, such as passage of satellites or spacedebris, super novas, etc., often remain unobserved.

A cost-efficient, high-resolution telescopic imaging system that has awide instantaneous-field of view, therefore, remains unrealized in theprior art.

SUMMARY OF THE INVENTION

The present invention enables telescopic imaging systems having largefields-of-view and high image resolution without some of the costs anddisadvantages of the prior art. Embodiments of the present invention areparticularly well suited for use in astronomical observation systems andaerial surveillance systems.

An illustrative embodiment of the present invention is a multiscaletelescopic imaging system comprising a monocentric reflective objectivelens and an array of microcameras. The objective lens images a sceneonto a spherical intermediate image surface. Each microcamera in themicrocamera array relays an image portion of the intermediate image ontoits respective focal-plane array while simultaneously correcting atleast one localized aberration in its image portion. The microcameras inthe microcamera array are arranged such that the fields of view ofadjacent microcameras overlap enabling field points of the intermediateimage to be relayed by multiple microcameras. As a result, a contiguousportion of the intermediate image is relayed, yet the camera arrayenables light from the scene to transit the array and reach theobjective lens. This mitigates obscuration and vignetting that commonlyplague conventional reflective imaging systems.

In some embodiments, the objective lens is a monocentric reflective lensthat includes a Schmidt corrector plate.

In some embodiments, the objective lens is a monocentric refractivelens.

In some embodiments, the objective lens is a refractive lens based on aDouble Gauss lens design.

An embodiment of the present invention is a multiscale telescopicimaging system comprising: an objective lens operative for forming anintermediate image of a scene, the intermediate image beingcharacterized by a first localized aberration; and a plurality ofmicrocameras, each microcamera comprising secondary optics and a focalplane array, the secondary optics being operative for relaying an imageportion of the intermediate image onto the focal plane array, whereineach microcamera is operative for reducing the magnitude of the firstlocalized aberration; wherein the system has a field of view that isequal to or greater than 10 degrees, and wherein the system hasresolution equal to or less than 2 arcseconds.

Another embodiment of the present invention is a multiscale telescopicimaging system comprising: an objective lens, the objective lens beingoperative for forming a first image of a scene at a first image surface;and a plurality of microcameras, each microcamera comprising a focalplane array, the plurality of microcameras being operative for relayinga plurality of image portions of the first image onto the plurality offocal plane arrays, wherein the plurality of microcameras is arranged ina first arrangement that enables the plurality of image portions tocollectively define a continuous region of the image, and wherein atleast one of the plurality of microcameras is operative for reducing themagnitude of a first localized aberration, and further wherein the firstarrangement enables at least a partial overlap of a first image portionand a second image portion of the plurality of image portions.

Another embodiment of the present invention is a multiscale telescopicimaging system comprising: an objective lens, the objective lens beingoperative for forming a first image of a scene at a first image surface,and the objective lens including at least one reflective surface; and aplurality of microcameras, each microcamera being operative for reducingthe magnitude of a first localized aberration, the plurality ofmicrocameras being operative for forming a plurality of image portionsof the first image, wherein the plurality of microcameras is arranged ina first arrangement of sub-groups, each sub-group comprising at leastone microcamera, and wherein the sub-groups are arranged in a secondarrangement that includes open space between at least two adjacentsub-groups.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a schematic drawing of a cross-sectional view of atelescopic imaging system in accordance with the prior art.

FIG. 2 depicts a schematic drawing of a cross-sectional view of amultiscale telescopic imaging system in accordance with an illustrativeembodiment of the present invention.

FIG. 3 depicts operations of a method for imaging a scene in accordancewith the illustrative embodiment of the present invention.

FIG. 4 depicts a schematic drawing of a cross-sectional view of amicrocamera in accordance with the illustrative embodiment of thepresent invention.

FIG. 5 depicts a modulation transfer function of an individualmicrocamera within system 200.

FIGS. 6A-D depict results of a Monte Carlo simulation of assemblytolerances for system 200.

FIG. 7A depicts a cross-sectional view of the modeled system.

FIG. 7B shows light rays for on-axis field 708.

FIG. 7C shows light rays of edge field 710.

FIG. 8 depicts a modulation transfer function for a reflectivemultiscale telescopic imaging system having a microcamera array arrangedin a HURA arrangement at the image plane.

FIG. 9 depicts a multiscale telescopic imaging system in accordance witha first alternative embodiment of the present invention.

FIGS. 10A-B depict spot diagrams and ray fans for system 200.

FIGS. 10C-D depict spot diagrams and ray fans for system 900.

FIG. 11 depicts the modulation transfer function of system 900.

FIGS. 12A-D depict Monte Carlo simulations of the performance of system900 under realistic manufacturing conditions.

FIG. 13 depicts a schematic drawing of a multiscale telescopic imagingsystem in accordance with a second alternative embodiment of the presentinvention.

FIGS. 14A-C depict spot diagrams of various imaged field points, theon-axis ray fan, and the paraxial chromatic focal shift for intermediateimage 1308.

FIG. 15 depicts microcamera 1310-i in accordance with the secondalternative embodiment of the present invention.

FIG. 16A shows an arrangement of two adjacent microcameras in accordancewith the second alternative embodiment of the present invention.

FIG. 16B shows the maximum angle subtended by a microcamera opticalassembly with respect to the center of objective lens 1302.

FIG. 17 depicts the modulation transfer function of sub-image 1526 atfocal-plane array 404 in system 1300.

FIGS. 18A-D depict Monte Carlo simulations of the performance of system1300 under realistic manufacturing conditions.

FIG. 19A depicts the relative illumination of microcamera 1310 byobjective lens 1302 as a function of field position.

FIG. 19B shows the chief ray angle of system 1300 as a function of fieldposition.

FIG. 20A depicts a schematic drawing of a perspective view of anarrangement of a microcamera array in accordance with the secondalternative embodiment of the present invention.

FIG. 20B depicts a detailed view of overlap fields 1316 formed by theoverlap of adjacent image portions 1314.

FIG. 21 depicts a schematic drawing of a cross-sectional view of amultiscale telescopic imaging system in accordance with a thirdalternative embodiment of the present invention.

FIGS. 22A-E depicts ray fans for five field positions withinintermediate image 2108.

FIG. 23 depicts the modulation transfer function of objective lens 2102as a function of field position.

FIG. 24 depicts a microcamera in accordance with the third alternativeembodiment of the present invention.

FIGS. 25A and 25B depict modulation transfer functions for system 2100with a microcamera on-axis and off axis, respectively.

FIGS. 26A and 26B depict the field curvature and distortion,respectively, of sub-image 2426-i at focal plane array 2404.

FIG. 27 depicts the relative illumination of sub-image 2426-i.

FIG. 28 depicts a schematic drawing of a cross-sectional view of amultiscale telescopic imaging system in accordance with a fourthalternative embodiment of the present invention.

FIG. 29 depicts a microcamera in accordance with the fourth alternativeembodiment of the present invention.

FIG. 30 depicts a modulation transfer function of an image portion 2814.

FIGS. 31A-D depict Monte Carlo simulations of the performance of system2800 under realistic manufacturing conditions.

DETAILED DESCRIPTION

FIG. 1 depicts a schematic drawing of a cross-sectional view of atelescopic imaging system in accordance with the prior art. Imager 100comprises primary mirror 102, secondary mirror 104, focusing system 106,and focal plane array 108. Imager 100 forms an image of a portion ofscene 110. Imager 100 is representative of restricted-view,large-aperture telescopes, such as the Sloan Digital Sky Surveytelescope, designed to generate a map of the entire sky. Image 100combines employs a wide aperture to enable astronomical surveys thatinclude stellar and galactic objects, as well as near-earth objects(e.g., low-earth satellites, space debris, etc.).

Primary mirror 102 is a 2.5-m diameter concave mirror that includes hole114. Primary mirror 102 has a substantially symmetric shape about axisof rotation 116. Mirror 102 receives light rays 112 from scene 110 andreflects them to secondary mirror 104.

Secondary mirror 104 is a 1.08-m diameter convex mirror having asubstantially symmetric shape about axis of rotation 116. Secondarymirror 104 receives light rays 112 from primary mirror 110 and reflectsthem to focusing system 106 through hole 114.

Light rays 112 are received from secondary mirror 104 at focusing system106, which forms an image on the surface of focal plane array 108.

Focal plane array 108 is conventional array of image sensors (e.g., CMOSsensors, CCD elements, infrared light photodetectors, etc.) thatconverts the received light into a digital representation of scene 110.

One skilled in the art will recognize that off-axis aberrations increaserapidly with field angle. Since primary mirror 102 and secondary mirror104 must correct both on- and off-axis aberrations, including sphericalaberration and coma, in order to mitigate the effects of off-axisaberrations, the instantaneous field of view of imager 100 is restrictedto an included angle of 2*θ1. For imager 100, θ1 is limited toapproximately 1.5 degrees, yielding an instantaneous field of view ofapproximately 3° over the approximately 4 m² collection area of theimager. As a result, the etendue of imager 100 (i.e., the area of thesystem aperture multiplied by the solid angle subtended, as seen fromthe aperture) is approximately 0.0086 Sr·m².

In comparison to other prior-art telescopic imaging systems, thethree-degree field of view of imager 100 is quite large. For example,the Keck telescope, located at the summit of Mauna Kea in Hawaii, has aninstantaneous field of view that is approximately 2 arcseconds by 8arcseconds. For many applications, however, a field of view of threedegrees is still insufficient since it restricts visibility to only asmall portion of a scene at any one time, thereby precluding observationof transient events that occur outside of the instantaneous viewableregion.

As discussed above, the goal of a telescopic imaging system is typicallyto achieve a resolution at the limit permissible by scintillation whileimaging the largest solid angle permissible by atmospheric seeingconsiderations. It has been shown that, for a Fried parameter of r₀=10cm, the minimum resolvable feature is 1 arcsecond for visible light. Inorder to achieve the desired resolution, the entrance pupil diameter ofthe camera is approximately the same size as the Fried parameter.

Monocentric objective lenses, in theory, promise the potential for largefields of view, since the field of view of a monocentric lens is limitedonly by vignetting. While monocentric reflective and catadioptricobjective-based telescopic imaging systems have been demonstrated, ithas proven difficult to achieve large fields of view in practice.Catadioptric telescopes have proven difficult to achromatize and usuallyrequire an objective mirror significantly larger than the entrancepupil. Refractive designs do not have this disadvantage; however,aperture obscuration in a reflective telescope can give rise vignetting,which increases at higher field angles. Further, chromatic aberrationsin a very large refractive objective are considerable and can bedifficult to correct.

The present invention, on the other hand, enables telescopic imagingsystems having resolution nearly at the atmospheric limit with greatlyincreased instantaneous fields of view and smaller apertures.Embodiments of the present invention attain these characteristics byemploying the multiscale imaging concept that is described in U.S. Pat.No. 8,259,212, which is incorporated herein by reference.

The Multiscale Imaging Approach

As disclosed in U.S. Pat. No. 8,259,212, a multiscale optical systemcomprises a single objective lens (which can be either a monocentriclens or a non-monocentric lens) and an array of microcameras, each ofwhich includes a one or more lenses and a focal-plane array. Theobjective lens and the microcameras divide the task of imaging a scene.The objective forms an imperfect intermediate image of the scene, wherethe intermediate image includes localized aberrations. The microcamerasrelay portions of the intermediate image onto their respectivefocal-plane arrays, while also reducing the localized aberrations, toyield a plurality of highly resolved optical sub-images. The focal-planearrays convert the plurality of optical sub-images into digitalsub-images of the relayed portions of the scene, which are thenprocessed to form a composite digital image of the entire scene.

The multiscale imaging approach affords advantages over other imagingapproaches. First, the collecting and processing functions afforded bythe objective lens and microcameras, respectively, can be individuallyimproved without significantly compromising the design of the other. Italso enables a large-scale objective lens to be used with a large-countmulti-aperture array, thereby reducing the trade-off between geometricaberration and instantaneous field of view.

The multiscale imaging approach also enables adjacent microcameras togenerate sub-images of overlapping portions of the scene. This can beused to ensure that light from a given point is always captured by atleast one microcamera. As a result, a multiscale imaging system caneliminate blind spots due to obscuration, such as those typically foundin reflective imaging systems.

Second, by providing wavefront correction at the optics of themicrocameras to correct aberrations introduced by atmosphericperturbation and/or the large-scale objective lens, the designcomplexity of the objective lens can be significantly reduced. This alsoenables faster collection optics, which reduces overall system volume.

Third, multiscale imaging is capable of improved image resolution.

Fourth, manufacturing cost and complexity can be significantly lower fora multiscale imaging system. Smaller lenses are better at providingwavefront correction because: 1) wavefront correction and imageformation both yield geometric solutions with less wavelength-scaleerror over smaller apertures; and 2) manufacturing of complex lenssurfaces is much easier in smaller scale systems.

Fifth, as described in U.S. patent application Ser. No. 13/889,007,filed May 7, 2013 (Attorney Docket: 525-004US2) and which isincorporated herein by reference, a multiscale imaging system withmicrocameras having one or more controllable camera settings (e.g.,focus, exposure, gain, magnification, dynamic range, etc.) enables themicrocameras to focus at diverse ranges with overlapping image regions.In other words, different microcameras can image different depths withinthe three-dimensional image field provided by the objective lens.Controllable magnification enables control over the amount of overlapbetween the images formed by different cameras. As a result, portions ofthe scene can be imaged by multiple cameras having differentillumination level, dynamic range, color filtering, etc. By employingvarious configurations of focus, exposure, gain, and dynamic range amongthe microcameras, a composite image can be reconstructed such that ithas enhanced depth-of-field, enhanced dynamic range, includestomographic object reconstruction, is substantially three-dimensional,and/or includes parallax views of the scene.

In addition, including dynamic camera settings in the microcamerasenables imaging systems in accordance with the present invention tocompensate for misalignment during assembly or environmentalperturbations, such as dynamic effects caused by wind, temperaturechanges, vibration, shock, and the like.

FIG. 2 depicts a schematic drawing of a cross-sectional view of amultiscale telescopic imaging system in accordance with an illustrativeembodiment of the present invention. System 200 includes objective lens202 and microcamera array 204. System 200 is a multiscale imaging systemdesigned to operate at wavelengths within the range from approximately486 nm to approximately 656 nm. System 200 provides high-resolutionimaging capability over a large instantaneous field of view—as large as60°—and has an aperture of 0.0079 m²for an etendue of 0.0067 Sr·m².System 200 includes 4272 microcameras, which operate in a mannerequivalent to 4272 telescopes, each having a 1.15° field of view. Whilethere are challenges utilizing the relatively small aperture of system200, the large instantaneous field of view enables observation of manyastronomical phenomena that might otherwise go unrecorded because system200 enables large swaths of the sky to be continuously monitored. Inaddition, system 200 is small enough that equatorial mounting ispossible. As a result, long exposures that compensate for siderealmotions could be more readily achieved for a wide field.

FIG. 3 depicts operations of a method for imaging a scene in accordancewith the illustrative embodiment of the present invention. Method 300begins with operation 301, wherein objective lens 202 forms intermediateimage 208.

Objective lens 202 is a monocentric reflective lens having asubstantially spherical shape. Objective lens 202 has an aperture ofapproximately 150 mm and a focal length of approximately 600 mm.Objective lens 202 forms intermediate image 208 such that theintermediate image has a substantially spherical shape having a radiusof approximately 600 mm. One skilled in the art will recognize thatintermediate image 208 is typically characterized by significantspherical aberrations but little or no chromatic aberrations. Objectivelens 202 is designed to image light rays received from scene 110 over aninstantaneous field of view equal to 2*θ2, where θ2 is as large as 30°.It should be noted that, in some embodiments, objective lens 202 enablesinstantaneous fields of view larger than 60°; however, in theillustrative embodiment, θ2 is limited to 7° to mitigate the deleteriouseffects of atmospheric aberrations, which increase as a function ofangle from zenith.

At operation 302, microcamera array 204 relays image portions 214 toform a plurality of sub-images of scene 110. Microcamera array 204comprises microcameras 210-1 through 210-N (referred to, collectively,as microcameras 210).

Microcamera array 204 is a two-dimensional array of N microcameras,which are arranged in an arrangement that substantially matches theshape of intermediate image 208. In the illustrative embodiment, N=4272;however, the value of N is design dependent. It is an aspect of themicrocamera array 204 that its arrangement includes gaps between themicrocameras that allow light from scene 110 to reach objective 202 soas to mitigate obscuration. Details of the arrangement of microcameraarray 204 is described below and with respect to FIGS. 7A-C.

It should be noted that, since objective lens 202 is monocentric, all ofits surfaces have the same center of curvature. As a result, theaberrations in intermediate image 208 are invariant with field angle andintermediate image 208 is formed on a spherical surface that is alsoconcentric with objective lens 202. The aberration invariance with fieldangle enables the use of the same optical design for each ofmicrocameras 210, which affords embodiments of the present invention thepotential for significantly lower cost.

It is an aspect of the present invention that microcameras 210 aredesigned and arranged such that light rays relayed to their respectivefocal plane arrays are incident on the focal plane array at near normalincidence to minimize magnification change when refocusing and tomitigate lateral chromatic aberration. As a result, each microcamera 210is aligned along a unique secondary optical axis 212 that issubstantially normal to its corresponding portion of intermediate image208.

FIG. 4 depicts a schematic drawing of a cross-sectional view of amicrocamera in accordance with the illustrative embodiment of thepresent invention. Microcamera 210-i is representative of each ofmicrocameras 210 and comprises relay optics 402 and focal plane array404. Microcamera 210-i relays image portion 214-i of intermediate image202 to form sub-image 426-i on focal plane array 404.

Relay optics 402 comprises lenses 406, 408, 410, 412, 414, and 416,which are arranged in four groups along secondary optical axis 212-i, aswell as stop 420 and conventional IR filter 422. Each of lenses 406,408, 410, 412, 414, and 416 is a molded plastic aspheric lens. Oneskilled in the art will recognize that the use of plastic lensesfacilitates mass production of microcameras 210. The materials used inrelay optics 402 include: N-BK7, having a refractive index of 1.515800and an Abbe Number of 64.167336; LF5, having a refractive index of1.581440 and an Abbe Number of 40.851305; E48R, having a refractiveindex of 1.531160 and an Abbe Number of 56.043828; and OKP4, having arefractive index of 1.607327 and an Abbe Number of 26.992638.

Table 1 in Appendix A provides a prescription for the design ofmicrocamera 210 in accordance with the illustrative embodiment. Thesedesign parameters realize a microcamera that, in concert with objectivelens 202, is designed to image at f/2.5, with the correspondingeffective f/# in the objective image space f/4 for diffraction limitedperformance with a 2.3 mm radius image at focal plane arrays 404 thatcorresponding to 1.15° in the sky (i.e., θ3=0.575). In some embodiments,at least one of lenses 406, 408, 410, 412, 414, and 416 comprises aglass (with suitable modification to the camera prescription), such asSchott N-BK7 crown glass or OHARA L-TIM28 flint glass, which wouldprovide improved homogeneity and decreased thermal variation as comparedto plastic lenses. In some applications, system 200 is operated in adifferent temperature range (e.g. a mountaintop) where temperaturecontrol is not possible. In such applications, optimization of the lenssurfaces for performance at a lower temperature is preferable. Further,the use of glass elements in such applications is also preferable, sinceglass typically has smaller thermal variation.

It should be noted that the design parameters for, and materials usedin, microcameras 210 provided are merely exemplary and it will be clearto one skilled in the art, after reading this Specification, how tospecify, make, and use alternative embodiments of the present inventionwherein objective lens 202 and microcameras 210 have any suitabledesign. It will be clear to one skilled in the art, after reading thisSpecification, how to specify, make, and use alternative embodimentswithout departing from the scope of the present invention.

Table 2 in Appendix A provides aspheric coefficients for theprescription provided in Table 1. Aspheric coefficients are based on aspherical reflective objective lens. The aspheric surfaces are designedto image at f/2.5 with diffraction limited performance with a 2.3-mmradius image at the focal plane array 404 (corresponding to 1.15° in thesky). The surface sag of an asphere is given by the formula:

${z(r)} = {\frac{r^{2}}{R\left( {1 + \sqrt{1 - \left( \frac{r}{R} \right)^{2}}} \right.} + {a_{2}r^{4}} + {a_{3}r^{6}} + {a_{4}r^{8}} + {a_{5}r^{10}}}$

Lenses 406 and 408 collectively define a first doublet that forms anapproximately collimated space into which the pupil is placed.

Lens 410 is a slightly converging element located near the pupil. Lens410 includes diffractive surface 424.

Lenses 412 and 414 collectively define a second doublet. Due to thermalvariations in the atmosphere, objective 202, and/or microcameras 210themselves, it is desirable that the microcameras be capable of moderaterefocusing. As a result, lenses 412 and 414 are arranged to be movablealong secondary optical axis 212-i. Mechanisms for enabling motion oflenses 412 and 414 are described in detail in U.S. patent applicationSer. No. 13/889,007.

Lens 416 is a meniscus lens that serves to form a flat field on thesensor.

Stop 420 is a paraxial stop located within microcamera 210 so that thestop effectively rotates with field angle. It is an aspect of thepresent invention that the inclusion of stop 420 mitigates off-axisvignetting in microcamera 210 at the periphery of the objective field.

It should be noted that diffractive surface 424 of lens 410 is locatednear stop 420 to enable color correction that is approximately the sameat both on- and off-axis field points. As a result, diffractive surface424 corrects chromatic aberration of the objective. Further, lens 410 isdesigned to be slightly converging to prevent vignetting of the rays onthe walls of the optical barrel (not shown for clarity) that containsrelay optics 402 and focal plane array 404.

One skilled in the art will recognize that atmospheric perturbations, aswell as the characteristics of objective lens 202, give rise tointermediate image 208 being characterized by localized aberrations. Itshould be noted that the arrangement of objective lens 202 andmicrocamera array 204 in system 200 provides a degree of compensationfor field curvature, which is a global aberration. For the purpose ofthis Specification, including the appended claims, a “global aberration”is defined as an aberration that extends, in slowly varying fashion,across multiple optical fields, such as field curvature. A “localizedaberration” is defined as an aberration, or a portion of a globalaberration, that is substantially unique to an individual optical field.For example, a plurality of localized aberrations might collectivelydefine a global aberration; however, the magnitude of wavefrontdistortion associated with each localized aberration is substantiallyunique to its associated individual optical field. Examples of localizedaberrations include spherical aberration, axial chromatic aberration,and spherochromatism.

At operation 303, each of microcameras 210 reduces a first localizedaberration in each of image portions 214.

For each microcamera 210, relay optics 402 is designed to correct atleast one localized aberration, such as spherical aberration, axialchromatic aberration, and/or spherochromatism, in the image portion itrelays to its respective focal-plane array 404. For the purposes of thisSpecification, including the appended claims, correcting an aberrationis defined as reducing its magnitude.

Chromatic aberration of objective lens 202 is corrected by diffractivesurface 424, which is included in lens 410. By placing diffractivesurface 424 near the paraxial stop (i.e., stop 420), color correction isapproximately the same at both on- and off-axis field points.

The phase of this diffractive surface (in radians) are given by theequation φ(r)=a₁r²+a₂r⁴+a₃r⁶, where the diffractive phase profilecoefficients are provided in Table 3 in Appendix A.

FIG. 5 depicts a modulation transfer function of an individualmicrocamera within system 200. It can be seen from plot 500 that theimaging performance of system 200 is largely diffraction limitedthroughout the field of view of a microcamera 210-i. The highest spatialfrequency corresponds to approximately 1.1 arcsec resolution.

One skilled in the art will recognize that manufacturing and assemblytolerances can make it challenging to maintain diffraction-limitedperformance at f/2.5. Typical microcamera assembly tolerances are ±25micron decenter, ±0.1° tilt placement, ±50 micron element thickness andlongitudinal displacement, 3 waves of power and 1 wave of irregularity.The RMS wavefront error, before and after these tolerances are applied,is 0.025 and 0.115 waves of error respectively.

FIGS. 6A-D depict results of a Monte Carlo simulation of assemblytolerances for system 200. Plots 600, 602, 604, and 606 show themodulation transfer function at field angles of 0, 0.3, 0.5, and 0.575degrees, respectively, with an average 0.085 waves of error over 50simulations which was consistent over many subsequent Monte Carlotrials.

At operation 304, sub-images 426 are converted into digital sub-images428 at focal plane arrays 404.

Focal plane array 404 is a two-dimensional array of CMOS sensors havinga pixel size of approximately 1.33 microns. The pixel size is small toenable many gigapixels in system 200. An example of a focal plane arraysuitable for use in microcamera 210 is the 1.4 μm pixel-pitch AptinaMT9F002 CMOS sensor, although other focal plane arrays, such as CCDarrays, can be used without departing from the scope of the presentinvention.

The radius of the sub-image formed on the focal plane array is 2.35 mm,which is constrained by the short dimension of the focal plane array.Because most commercial focal plane arrays have a rectangular ratherthan a square aspect ratio, the periphery of the focal plane array isnot illuminated and therefore is typically not sampled.

As discussed above, a challenge for using reflective optics intelescopic imaging systems is obscuration caused by the imaging surfaceitself. The wider the image field used, the more of the primary mirroraperture is blocked. For a sufficiently wide angle, this can result inthe center of the image being completely vignetted.

It is an aspect of some of embodiments of the present invention thathigh resolution and contrast of an image can be retained by placingmicrocameras 210 sparsely in the image plane with gaps between them toallow light from scene 110 to reach objective 202. In the illustrativeembodiment, therefore, microcamera array 204 is arranged in a hexagonaluniformly redundant array (HURA) having array parameters v and r areequal to 31 and 6, respectively. Such an arrangement of microcamerasminimizes the introduced nonuniformity in the modulation transferfunction due to the obscuration because such configurations produceautocorrelations, and therefore transfer functions, with minimalvariations in spatial frequency. In some embodiments, microcamera array204 is arranged in another arrangement comprising gaps betweenmicrocameras, such as a Golay non-redundant aperture.

FIGS. 7A-C depict a model of a multiscale telescopic imaging systemhaving a sparse arrangement of microcameras. The model is based on apattern of microcameras arranged in a hexagonal uniformly redundantarray with parameters v=31 and r=6. To model the vignetting of themicrocamera array, this pattern is transformed into an HURA aperture,located at the image plane, with circular holes in the aperturecorresponding to gaps between microcameras.

FIG. 7A depicts a cross-sectional view of the modeled system. System 700comprises reflective objective 702 and HURA aperture 704, which islocated at the image plane of objective 702. System 700 is analogous tosystem 200.

HURA aperture 704 includes circular holes 706, which correspond to gapsbetween microcameras 210 in microcamera array 204.

FIG. 7B shows light rays for on-axis field 708. These light rays passthrough HURA aperture 704 whereas, without holes 706, the light rays ofon-axis field 708 would be completely vignetted.

FIG. 7C shows light rays of edge field 710. Edge field 710 is onlypartially blocked by the HURA aperture and, therefore, is only partiallyvignetted by microcamera array 204.

FIGS. 8 depicts a modulation transfer function for a reflectivemultiscale telescopic imaging system having a microcamera array arrangedin a HURA arrangement at the image plane.

Plot 800 includes the effects of obscurations caused by microcameraarray 204. Plot 800 can be compared to plot 500, described above andwith respect to FIG. 5, which does not account for image planevignetting due to obscurations by microcamera array 204. Plot 800evinces that the vignetting of HURA aperture 704 causes a reduction inhigher spatial frequencies, however, a fairly uniform modulationtransfer function is still achieved. It should be noted that the flatmodulation transfer function is due to autocorrelation properties of theHURA arrangement. The highest spatial frequency corresponds to theNyquist sampling rate (i.e., 1.1 arcsec resolution).

As depicted in FIG. 2, microcameras 210 are designed and positioned inmicrocamera array 204 such that the image portions 214 of adjacentmicrocameras overlap in overlap regions 216. It is an aspect of thepresent invention that image portions of several microcamera-telescopescan be used to complement each other to compensate for obscurationand/or vignetting that can occur due to light blockage by themicrocameras themselves. In addition, overlap regions 216 enable pointsin these overlap regions to be relayed by more than one microcamera,which facilitates stitching digital sub-images 428 into compositedigital image 220.

It should be noted that splitting rays at the edge of the fields of viewof adjacent microcameras can cause tangential vignetting and acorresponding decrease in tangential resolution.

At operation 305, processor 218 receives digital sub-images 428-1through 428-N and stitches them together to form digital image 220.

FIG. 9 depicts a multiscale telescopic imaging system in accordance witha first alternative embodiment of the present invention. System 900comprises objective lens 202, microcamera array 904, and Schmidtcorrector plate 902. System 900 is analogous to system 200, but alsoincludes Schmidt corrector plate 902 to reduce spherical aberrations inintermediate image 908. The addition of Schmidt corrector plate 902requires alteration of the prescription for microcameras 910; however,the basic microcamera layout remains the same as that of microcamera210.

FIGS. 10A-B depict spot diagrams and ray fans for system 200.

FIGS. 10C-D depict spot diagrams and ray fans for system 900.

A comparison of plots 1000 and 1002 versus plots 1004 and 1006 showsthat the system 200 (i.e., a telescopic imaging system having aspherical mirror but no Schmidt corrector plate) exhibits significantspherical aberrations but no chromatic aberrations. System 900 (i.e.,system 200 including Schmidt corrector plate 902), on the other hand,exhibits a slight amount of spherochromatism. The Schmidt correctorintroduces off-axis aberrations and therefore is not truly monocentric,however, an instantaneous field of view of 10° is still readilyachievable.

Schmidt corrector plate 902 is an aspheric lens having sphericalaberration that is the complement (i.e., equal to, but opposite of, thespherical aberration of objective lens 202. Schmidt corrector plate 902corrects the paths of light rays 206 such that the light reflected fromthe outer part of the objective lens and light reflected from the innerportion of the objective lens is brought to the same focus.

Tables 4, 5, and 6 in Appendix A provide the prescription, asphericsurface coefficients, and diffractive phase polynomial, respectively,for system 900.

FIG. 11 depicts the modulation transfer function of system 900. Plot1100 shows the nominal modulation transfer function of a sub-imageformed at a focal plane array of a microcamera 910. It should be notedthat the highest spatial frequency corresponds to the Nyquist samplingrate or 1.1 arcsec resolution.

FIGS. 12A-D depict Monte Carlo simulations of the performance of system900 under realistic manufacturing conditions. Plots 1200, 1202, 1204,and 1206 show Monte Carlo modulation transfer functions at four fieldpoints (i.e., field angles of 0, 0.3, 0.5, and 0.575 degrees,respectively) after accounting for manufacturing tolerances simulatedfor the Schmidt camera objective monocentric multiscale camera. Thetolerances are ±25 micron surface and element decenter, 0.1° surface andelement tilt, and ±50 micron element-thickness and axial-placementtolerances.

Multiscale Schmidt telescopes have the advantage of relaxing the demandson the microcameras to correct aberrations at the expense of requiring alarge Schmidt corrector. It should be noted that these designs can bescaled to larger sizes, with a corresponding relaxation in thetolerances, and maintain 1.1 arcsec performance. Therefore microcamerasthat can be inexpensively mass produced can offset the additional costof fabricating large, well-corrected optical elements.

FIG. 13 depicts a schematic drawing of a multiscale telescopic imagingsystem in accordance with a second alternative embodiment of the presentinvention. System 1300 comprises objective lens 1302 and microcameraarray 1304.

System 1300 is a multiscale imaging system designed to operate atwavelengths within the range from approximately 486 nm to approximately656 nm. System 1300 provides high-resolution imaging capability(approximately 1.1 arcsec) over a 60° instantaneous field of view andhas a focal length of 251.3 mm.—and has an aperture of 0.0079 m² for anetendue of 0.0067 Sr·m². System 1300 includes 4272 microcameras, whichoperate in a manner equivalent to 4272 telescopes, each having a 1.15°field of view. The f/# of the image formed on the microcamera sensor isf/2.5, with the corresponding effective f/# in the objective image spacef/4. Operation of system 1300 is analogous to method 300 described aboveand with respect to system 200.

The prescription, aspheric coefficients, and the profile for diffractivesurface for system 1300 is provided in Tables 7, 8, and 9 in Appendix A,respectively.

Objective lens 1302 is a multi-element monocentric lens comprising lenselement 1306, entry lens shell 1318, and exit lens shell 1320.

Lens element 1306 is a partial sphere that includes hemispheres 1322 and1324, each of which comprises Schott N-BK7 glass.

Each of entry lens shell 1318 and exit lens shell 1320 is a monocentricmeniscus element that comprises Schott LF54 glass.

The glasses chosen for use in objective lens 1302 can be produced inlarge, homogeneous blanks with few striae and up to 300-mm thick using acontinuous melting process. The coefficients of thermal expansion of thetwo materials are fairly compatible, with LF5 being 9.1×10⁻⁶/° C. andN-BK7 7.1×10⁻⁶/° C., which is important given the large sizes of theelements. The thicknesses of the required slabs of LF5 in this designare limited to 290 mm as it is assumed that 5 mm must be sacrificed forpolishing on both faces of the slab.

The apertures of objective lens 1302 are oversized at 80° (rather thanat the design objective of a 60° instantaneous field of view). Thisavoids vignetting of the field in microcameras 1310.

It should be noted that the combination of crown glass and flint glassin objective 1302 enables correction of chromatic aberrations, with thecrown-glass lens element 1306 providing the positive power and the twoflint-glass meniscus elements (i.e., entry lens shell 1318 and exit lensshell 1320) providing negative power. In addition, the radii minimizethe spherical aberrations. The focal length of the f/4 objective lens is616 mm.

FIGS. 14A-C depict spot diagrams of various imaged field points, theon-axis ray fan, and the paraxial chromatic focal shift for intermediateimage 1308.

Plot 1400 shows the chromatic focal shift of objective 1302.

Plot 1402 shows the ray fan of an on-axis ray in system 1300, whichexhibits both spherical and chromatic aberrations.

Plot 1404 depicts spot diagrams formed by objective 1302 at off-axisangles of 0, 15, 30, and 40 degrees.

Plots 1400, 1402, and 1404 show that, over the wavelength range, thereis up to 0.3 mm of focal shift throughout the band from 0.486 to 0.656nm, which is much larger than the approximately 0.016 mm depth of fieldexpected for an f/4 lens. In addition, the ray fan shows a sphericalaberration of both 3rd and 5th order, with the rays deviating up to0.015 mm from the focal spot, which should be about 0.002 mm whendiffraction-limited. It is clear, therefore, that substantial axialchromatic and spherical aberrations are present. It should be noted thatthe secondary spectrum focal shift is 0.3 mm, the correction of whichrequires that each of microcameras 1310 include a diffractive element.

FIG. 15 depicts microcamera 1310-i in accordance with the secondalternative embodiment of the present invention. Microcamera 1310-i isanalogous to microcamera 210-i, described above and with respect to FIG.4; however, the elements of microcamera 1310-i are designed foroperation in a refractive telescopic imaging system comprising objectivelens 1302. Microcamera 1310-i is representative of each of microcameras1310-1 through 1310-N.

Microcamera 1310-i includes relay optics 1502 and focal plane array 404.Relay optics 1502 includes lens elements 1506, 1508, 1510, 1512, 1514,and 1516, as well as IR filter 422. Microcamera 1310-i is designed toprovide substantially the same instantaneous field of view asmicrocamera 210-i.

Each microcamera 1310-i corrects aberrations of objective lens 1302 inits respective image portion 1314-i and relays it to focal plane array404 as sub-image 1526-i. These aberrations are of three types. First,intermediate image 1308 is curved, the curvature of field is correctedso that the image is formed on a flat sensor. As discussed above, fieldcurvature is a global aberration.

Second, spherical aberrations in image portion 1314-i are corrected.Spherical aberration is a localized aberration that is a geometricaberration. Spherical aberration is corrected by relay optics 1502 viathe inclusion of aspheric surfaces.

Finally, intermediate image 1308 includes axial chromatic aberrations.These aberrations are also localized aberrations that are second-orderand large in magnitude. System 1300 corrects these aberrations viadiffractive surface 1524, which provides a large amount of chromaticdispersion with a partial dispersion very different than availableoptical materials.

While there are some diffraction efficiency losses, the large dispersionof diffractive surface 1524 can offset the large secondary chromaticaberration of objective 1302. This makes a diffractive an attractivechoice for chromatic control despite its disadvantages. In someembodiments, correction of combinations of spherical and chromaticaberrations (e.g. spherochromatism) is included in microcamera 1310-i.

Like microcamera array 204, discussed above and with respect to FIG. 2,microcameras 1310 are designed and positioned in microcamera array 1304such that adjacent microcameras can relay overlap regions 1316. Raysfrom field points in overlap regions 1316 are divided between adjacentmicrocameras so that an image may be formed in each microcamera. As aresult, each of the multiple sub-images that are formed have only afraction of the illumination of the original source point, and also hasdecreased resolution due to only partially filling the aperture of eachcamera.

FIG. 16A shows an arrangement of two adjacent microcameras in accordancewith the second alternative embodiment of the present invention.Microcameras 1310-i and 1310-i+1 are arranged side-by-side with focusedfield points of intermediate image 1308 being relayed to focal-planearrays 404-i and 404-i+1. Overlap region 1316-i is split betweenmicrocameras 1310-i and 1310-i+1.

FIG. 16B shows the maximum angle subtended by a microcamera opticalassembly with respect to the center of objective lens 1302. The coneangle, θ6, determines how closely microcameras 1310-i and 1310-i+1 canbe located. If microcameras 1310-i and 1310-i+1 are placed so that theangle their optical axes 1312-i and 1312-i+1 subtend with respect to thecenter of objective lens 1302 is less than cone angle θ6, the twomicrocameras will mechanically interfere. As a result, it is desirableto design microcameras 1310 with the largest possible field size 1314while maintaining the minimum cone angle to maximize the size of overlapregions 1316.

As discussed above, in some embodiments, overlap regions 1316 enable theuse of microcamera-telescopes that complement each other to compensatefor obscuration and/or vignetting that can occur due to light blockageby the microcameras themselves. In addition, overlap regions 1316 enablepoints in these overlap regions to be relayed by more than onemicrocamera, which facilitates stitching digital sub-images 1528 intocomposite digital image 220.

FIG. 17 depicts the modulation transfer function of sub-image 1526 atfocal-plane array 404 in system 1300. Plot 1700 shows that theperformance of objective lens 1302 is slightly decreased from thatobjective lens 202 (with or without Schmidt corrector plate 902). Afteraccounting for the effects of obscuration in the reflective objectivelens systems, however, the performance of objective lens 1302 is betterin some cases. It should be noted that the highest spatial frequencycorresponds to the Nyquist sampling rate (i.e., 1.1 arcsec resolution).

FIGS. 18A-D depict Monte Carlo simulations of the performance of system1300 under realistic manufacturing conditions. Plots 1800, 1802, 1804,and 1806 depict Monte Carlo modulation transfer functions, accountingfor assembly and fabrication tolerances, at angles of 0, 0.3, 0.5, and0.575 degrees, respectively. The simulations are based on Monte Carlomodulation transfer functions from a simulation of 50 randomizedassembly error instruments, while accounting for assembly tolerances of±25 micron decenter, ±0.1° tilt placement, ±50 micron element thicknessand longitudinal displacement, 3 waves of power and 1 wave ofirregularity. Examination of plots 1800, 1802, 1804, and 1806 revealsthat the RMS wavefront error, before and after these tolerances areapplied, is 0.075 and 0.145 waves of error respectively. The average RMSwavefront error over the Monte Carlo trials is 0.115 waves and isconsistent over the Monte Carlo runs.

FIG. 19A depicts the relative illumination of microcamera 1310 byobjective lens 1302 as a function of field position. Plot 1900 showsthat the amount of light entering microcamera 1310 decreases as thefield angle increases, because more of the illumination is captured bythe neighboring cameras.

FIG. 19B shows the chief ray angle of system 1300 as a function of fieldposition. Plot 1902 includes traces 1904 and 1906, which denote thesagittal and tangential rays, respectively. The chief ray angle ismaintained within 3° of normal throughout the field. It should be notedthat a chief ray angle near normal incidence minimizes variations inmagnification caused by refocusing. As discussed above, somemicrocameras in accordance with the present invention include dynamicfocus to enable compensation for effects such as thermal variations orchromatic aberrations.

FIG. 20A depicts a schematic drawing of a perspective view of anarrangement of a microcamera array in accordance with the secondalternative embodiment of the present invention. Arrangement 2000includes 4272 microcameras 1310, which are arranged on a hexagonal grid.Image portions 1314 are separated by an angle within the range ofapproximately 0.87° to approximately 0.94° on intermediate image 1308.Unequal spacing of image portions 1314 is required as there is noregular tiling of the sphere above 12 vertices. The maximum field angleis 0.575°, so that there is a 0.105° angle of overlap of microcamera1310 with its neighbors (excluding positioning error).

It should be noted that image fields 1314 are arranged on a hexagonalgrid because the solid angle covered by the array is not large enough torequire an icosahedral geodesic packing.

FIG. 20B depicts a detailed view of overlap fields 1316 formed by theoverlap of adjacent image portions 1314.

Refractive multiscale telescopic imaging systems afford some advantagesover reflective multiscale telescopic imaging systems. First,aberrations to the optical path delay due to glass inhomogeneity thatcould be tolerated increases in proportion to scale (as long as theresolution of the system remains constant). Second, a refractivemultiscale telescopic imaging system avoids the obscuration issuesdescribed above. As a result, a refractive multiscale telescopic imagingsystem can increased etendue over a refractive multiscale telescopicimaging system having the same entrance pupil diameter. Third,microcameras are easier to mount in a refractive multiscale telescopicimaging system, since there is no a need to consider obscurations.

One skilled in the art will recognize that an important considerationfor any imaging system is etendue. For some embodiments of the presentinvention, increasing etendue requires scaling the diameter of theentrance pupil and therefore the overall size of the optical system,including the scale of all elements of the objective, microcamera, andthe focal-plane array. Since the mass of the optical system scales withthe scale cubed, the cost of the optics for a refractive multiscaletelescopic imaging system can increase rapidly with increasing scale.Furthermore, it is challenging to fabricate a monocentric refractiveobjective lens larger than objective lens 1302. The lens elements thatcompose objective lens 1302 are formed from glass blanks. Unfortunately,as the thickness of a glass blank increases beyond approximately 300 mm,it is with difficult, if not impossible, to achieve sufficienthomogeneity through its bulk.

FIG. 21 depicts a schematic drawing of a cross-sectional view of amultiscale telescopic imaging system in accordance with a thirdalternative embodiment of the present invention. System 2100 comprisesobjective lens 2102 and microcamera array 2104. System 2100 is analogousto system 1300; however, objective lens 2102 is not a monocentricobjective lens and, therefore, avoids the thickness limitation for glassblanks described above. System 2100 has an instantaneous field of viewof 25 degrees (i.e., θ7 is equal to 12.5°).

Objective lens 2102 is a refractive lens based on a double-gauss lensdesign. The elements of objective lens 2102 are limited to less than 150mm in diameter and less than 4 mm in thickness. Objective lens 2102,therefore, can be readily fabricated using conventional commerciallyavailable glass blanks. Table 10, provided in Appendix A, provides aprescription for objective lens 2102. For the purposes of illustrationherein, the materials designated in Tables 10 and 11 are commerciallyavailable materials from OHARA glass.

Objective lens 2102 is substantially symmetric about a central stop;therefore, the lens is substantially coma- andlateral-chromatic-aberration-free. As a result, in similar fashion to amonocentric objective lenses 202 and 1302, residual aberrations inintermediate image 2108 are substantially limited to sphericalaberration, axial chromatic aberration, and curvature of field.

FIGS. 22A-E depicts ray fans for five field positions withinintermediate image 2108. Plots 2200, 2202, 2204, 2206, and 2208 show rayfans for field angles of 0, 5, 10, 15, and 18 degrees, respectively. Itcan be seen from the plots that the aberrations are substantiallyinvariant with field angle. Further, the aberrations are odd-symmetric,which is consistent with spherical aberration. It should be noted thatthe center of intermediate image 2108 does not coincide with the stopplacement, although this image surface is spherical.

FIG. 23 depicts the modulation transfer function of objective lens 2102as a function of field position.

It is an aspect of the present invention that the design of objectivelens 2102 ensures that the chief ray is perpendicular to intermediateimage 2108 along is curved image surface. This is in similar fashion tothe monocentric multiscale telescopic imaging systems described above.By ensuring this relationship, image rays enter each of microcameras2110 at substantially normal incidence, which mitigates vignetting inthe microcameras.

FIG. 24 depicts a microcamera in accordance with the third alternativeembodiment of the present invention. Microcamera 2110-i comprises relayoptics 2402 and focal-plane array 2404. Microcamera 2110-i is analogousto microcamera 1310-i, described above and with respect to FIGS. 13 and15. A prescription for microcamera 2110-i is provided in Table 11, foundin Appendix A. Microcamera 2110-i has a cone angle of approximately1.386° (i.e., θ8 is 0.693°) and can image out to a maximum of 1 degreeoff axis. Lens elements included in relay optics 2402 comprise plasticmaterials (e.g., Zeonex E48R and Osaka Gas Chemicals OKP4), although itwill be clear to one skilled in the art, after reading thisSpecification, how to specify, make, and use one or more glass elementsin microcamera 2110-i.

The track length of objective lens 2102 is approximately 480 mm andmicrocamera 2110-i has a track length of approximately 108 mm. Eachmicrocamera telescope has a IFOV of 9 microrads.

Focal plane array 2404 includes a two-dimensional array of 1.4-micronpixel elements, providing system 2100 with approximately 2.5 gigapixelsof resolution.

FIGS. 25A and 25B depict modulation transfer functions for system 2100with a microcamera on-axis and off axis, respectively. Plot 2500 showsthe modulation transfer function for system 2100 with microcamera 2110-ion-axis. Plot 2502 shows the modulation transfer function for system2100 with microcamera 2110-i off-axis by 8°.

FIGS. 26A and 26B depict the field curvature and distortion,respectively, of sub-image 2426-i at focal plane array 2404.

FIG. 27 depicts the relative illumination of sub-image 2426-i. Plot 2700shows that illumination is substantially uniform except at the edge(i.e., in overlap regions 2116), where its light is divided amongadjacent microcameras.

FIG. 28 depicts a schematic drawing of a cross-sectional view of amultiscale telescopic imaging system in accordance with a fourthalternative embodiment of the present invention. System 2800 is acatadioptric imaging system that comprises objective lens 2802 andmicrocamera array 2804. System 2800 is analogous to system 200. System2800 has an instantaneous field of view of 15 degrees (i.e., θ8 is equalto) 7.5° and 1.1 arcsec resolution. A prescription for system 2810 isprovided in Table 12 in Appendix A. System 2800 is designed foroperation at wavelengths within the range of approximately 486 nm toapproximately 656 nm.

Objective lens 2802 is a reflective lens having a substantiallyspherical shape. Objective lens 2802 has a radius of 3048 mm and adiameter of 762 mm (f/2). Its field of view is approximately 15°.

Microcamera array 2804 includes 88 substantially identical microcameras2810-1 through 2810-N (where N=88), which operate as the equivalent of88 200-mm individual telescopes.

FIG. 29 depicts a microcamera in accordance with the fourth alternativeembodiment of the present invention. Microcamera 2810-i is adouble-gauss design that comprises relay optics 2902 and focal-planearray 2904. Microcamera 2810-i is analogous to microcamera 210-i,described above and with respect to FIG. 4. Microcamera 2810-i has acone angle of approximately 0.6° (i.e., θ9 is equal to 0.3°).

Relay optics 2902 are based on a Double Gauss design that is modified torelay at finite conjugates and includes entrance lens 2906, which isdesigned to prevent rays from vignetting into the system.

The f/# at focal-plane array 2904 is 2.25, and the rays are image-sidetelecentric and so the chief ray angle is normal to focal-plane array2904. The rear two elements are movable along microcamera axis 2812-i toenable refocus of microcamera 2810-i. As discussed above, dynamic focuscapability for the microcameras of a multiscale telescopic imagingsystem enables compensation for thermal variations, as well asmanufacturing tolerances; however, the telecentricity of microcamera2810-i ensures the same magnification through the focus range.

Focal-plane array 2904 comprises a two-dimensional array of image pixelsthat are within the range of approximately 1.5 microns to 2.2 microns insize. Typically, focal-plane array 2904 includes approximately 5megapixels. In some embodiments, focal-plane array 2904 includes 14megapixels in 2×2 binning mode. The instantaneous field of view ofsystem 2800 is given by the pixel size of the focal-plane array 2904divided by the effective focal length of the system 2800 as determinedby the combination of objective lens 2802 and microcamera 2804, whichshould be equal to the desired sampling of the image of 1.1 arcseconds(equivalently 5.33 microradians).

Objective lens 2802 images scene 110 at intermediate image 2808. The 15°field of view allows for segmentation of intermediate image 2808 into176 separate fields of view—each having a diameter of approximately0.48°. As mentioned above, each microcamera in microcamera array 2804has a field of view of approximately 0.6, which enables the microcamerasto be spaced apart by 0.48° but yields overlap regions 2816 that containbetween 10% and 25% of adjacent image portions 2814. As a result, the 88microcameras can be arranged in a sparse arrangement (e.g., half filled)to provide open regions between them. These open regions enable lightfrom scene 110 to reach objective lens 2802, yet the microcamerascollectively relay the entire intermediate image onto their focal-planearrays. Further, it also enables overlap of adjacent image portions 2814to create overlap regions 2816, which affords advantages to system 2800,as discussed above. It should be noted that the telecentricity ofmicrocameras 2810 ensures that overlap regions 2816 contain the sameimage points as the focus of one or more of the microcameras is changed.

FIG. 30 depicts a modulation transfer function of an image portion 2814.Plot 3000 shows that good optical performance is maintained out to theedge of image portion 2814, where it becomes an overlap region 2816,where another microcamera can form a higher-quality image.

FIGS. 31A-D depict Monte Carlo simulations of the performance of system2800 under realistic manufacturing conditions. The assumptions forcomponent and manufacturing tolerances for the simulations are±25-micron surface and element decenter, ±50-micron element thicknessand axial placement, and 0.1° surface and element tilt.

Plots 3102, 3104, 3106, and 3108 show the Monte Carlo MTF, maintainingthe performance at 200 cycles/mm.

Given the large number of components in each of the multiscaletelescopic imaging systems described herein, manufacturability isimportant as is amenability to mass production techniques. Forastronomical applications of system 2800, the estimated limitingmagnitude of each image portion 2814 is estimated to be 19.7 (assuming a300 second exposure period of 30 stacked 10-second exposures with 15photoelectrons noise per acquired image). Since the field of view ofsystem 2800 is 15°, parts of the field may be exposed up to 3600seconds, allowing the magnitude to 21. Further, near-Earth objects canbe found by stacking partial exposures at the non-sidereal rate.

It is expected that the entire night sky could be monitored continuouslyby a world-wide network of multiscale telescopic imaging systemsdirected near the zenith. This would require approximately 480 copies ofsystem 2800, for example, which would be the equivalent of 42,240eight-inch telescopes or 144 gigapixels. A simple equatorial platformclock-drive mechanism would suffice for sidereal tracking, greatlysimplifying mounting. Furthermore, as microcamera designs continue toimprove, the modular multiscale design enables straight-forward systemupgrades, so improvements could leverage existing infrastructure.

It is to be understood that the disclosure teaches just one example ofthe illustrative embodiment and that many variations of the inventioncan easily be devised by those skilled in the art after reading thisdisclosure and that the scope of the present invention is to bedetermined by the following claims.

Appendix A

TABLE 1 Prescription for microcamera 210. Radius R Thickness DiameterSurface # (mm) (mm) Material (mm) Comment 1 26.63415 3 E48R 9.6Microcamera start, Aspheric Surface 2 −22.69573 3 OKP4 9.6 3 −59.1869922 9.6 Aspheric Surface 4 ∞ 0.5 N-BK7 6.965157 Stop, IR cut filter 5 ∞ 18.004592 6 200 2 E48R 8.134189 Lens 410 7 −50 10.00982 8.272826Diffractive surface 8 53.41197 2.5 OKP4 9.819086 Focusing element Lenses412, 414 9 10.48588 3.5 E48R 10.0174 10 −26.70599 4 10.24507 11 7.2573489 E48R 10.16389 Aspheric Surface (L6) 12 4.269028 2 5.997253 MicrocameraEnd, Aspheric Surface 13 ∞ 0.4 N-BK7 5.74972 Sensor window 14 ∞ 0.15.698356 15 ∞ 4.680515 Image plane

TABLE 2 Aspheric coefficients for the prescription for microcamera 210(Table 1 above). a₂r⁴ coefficient a₃r⁶ coefficient a₂r⁸ coefficienta₂r¹⁰ coefficient Surface # (mm⁻³) (mm⁻⁵) (mm⁻⁷) (mm⁻⁹) 1 −1.6886523 ×10⁻⁵   1.7786764 × 10⁻⁶ −8.9893941 × 10⁻⁸  1.553034 × 10⁻⁹ 3 2.2745659 ×10⁻⁵ −1.2045343 × 10⁻⁷ 2.9732628 × 10⁻⁹ 0 11 −8.219397 × 10⁻⁵ −1.5610208× 10⁻⁶  1.9589715 × 10⁻¹⁰ 0 12 −0.00097436575 −0.00015217878 0 0

TABLE 3 Diffractive phase profile coefficients for diffractive surface424. a₁r² coefficient a₂r⁴ coefficient a₃r⁶ coefficient Surface # (mm⁻²)(mm⁻⁴) (mm⁻⁶) 7 −57181.552 3732654.7 2.9919161 × 10⁹

TABLE 4 Prescription for system 900. Radius Thickness Diameter Surface #(mm) (mm) Material (mm) Comment 1 ∞ ∞ 0 Object 2 ∞ −5 N-BK7 150 Schmidtcorrector plate, Aspheric Surface 3 ∞ −1196.725 150 4 1200 600 MIRROR358 Spherical primary mirror 5 598.464 40 104 Intermediate image surface6 26.54865 3 E48R 9.6 Microcamera start, Aspheric Surface (Lenses 406,408) 7 −22.47182 3 OKP4 9.6 8 −58.99699 22 9.6 Aspheric Surface 9 ∞ 0.5N-BK7 6.967818 Stop, IR cut filter 10 ∞ 1 8.007911 11 200 2 E48R8.139009 Lens 410 12 −50 9.869349 8.28092 Diffractive Surface 1353.40306 2.5 OKP4 9.817042 Focusing element (Lenses 412, 414) 1410.54498 3.5 E48R 10.01713 15 −26.70153 4 10.24834 16 7.377223 9 E48R10.17653 Aspheric Surface (Lens 416) 17 4.339543 2 5.978056 MicrocameraEnd, Aspheric Surface 18 ∞ 0.4 N-BK7 5.745812 Sensor window 19 ∞ 0.15.697902 20 ∞ 4.681273 Image plane

TABLE 5 Aspheric coefficients of the prescription for system 900. a₂r⁴coefficient a₃r⁶ coefficient a₂r⁸ coefficient a₂r¹⁰ coefficient Surface# (mm⁻³) (mm⁻⁵) (mm⁻⁷) (mm⁻⁹) 1     2.69 × 10⁻¹⁰    2.005 × 10⁻¹⁵  −1.492 × 10⁻¹⁹ 0 6 −3.0537948 × 10⁻⁵  1.5739492 × 10⁻⁶ −1.0680456 ×10⁻⁷  2.0248597 × 10⁻⁹ 8  1.3621198 × 10⁻⁵ −7.4489343 × 10⁻⁷ 9.4868098 ×10⁻⁹ 0 16 −3.7950446 × 10⁻⁵ −9.0816072 × 10⁻⁷ 9.3362672 × 10⁻⁹ 0 17−0.00088357931 −9.2151543 × 10⁻⁵ 0 0

TABLE 6 Diffractive phase profile coefficients for diffractive surface424 in system 900. a₁r² coefficient a₂r⁴ coefficient a₃r⁶ coefficientSurface # (mm⁻²) (mm⁻⁴) (mm⁻⁶) 12 −54883.335 2865723.7 1.7517389 × 10⁻⁹

TABLE 7 Prescription for system 1300. Radius Thickness Diameter Surface# (mm) (mm) Material (mm) Comment 1 ∞ ∞ 0 Object 2 360 217.243 LF5543.826 Objective start 3 142.757 142.757 N-BK7 241.668 4 ∞ 142.757N-BK7 241.668 5 −142.757 232.121 LF5 229.566 6 −374.878 240.397 518.064Objective end 7 −615.275 40 13.41169 Intermediate image surface 827.74976 5 E48R 9.6 Microcamera start, Aspheric Surface (Lenses 1406 and1408) 9 −88.49545 5 OKP4 9.6 10 −61.66614 26.32681 9.6 Aspheric Surface11 ∞ 0.5 N-BK7 6.657188 Stop, IR cut filter 12 ∞ 1 7.721244 13 200 2E48R 7.949465 (Lens 1410) 14 −50 9.705121 8.207923 Diffractive surface15 48.58209 2.5 OKP4 9.840211 Focusing element (Lenses 1412 and 1414) 16−55.33565 2.5 E48R 9.930473 17 −24.29105 4 10.01174 18 7.573737 6 OKP49.17504 Aspheric Surface (Lens 1416) 19 4.455139 2 6.143487 Microcameraend, Aspheric Surface 20 ∞ 0.4 N-BK7 5.801741 Sensor window 21 ∞ 0.15.728899 22 ∞ 4.706103 Image plane

TABLE 8 Aspheric coefficients of the prescription for system 1400. a₂r⁴coefficient a₃r⁶ coefficient a₂r⁸ coefficient a₂r¹⁰ coefficient Surface# (mm⁻³) (mm⁻⁵) (mm⁻⁷) (mm⁻⁹) 8 5.1324798 × 10⁻⁵ −4.3508909 × 10⁻⁶1.8669263 × 10⁻⁷  −3.5385648 × 10⁻⁹ 10 5.9766855 × 10⁻⁵ −2.4961897 ×10⁻⁶ 4.532904 × 10⁻⁸ 0 18 0.00016230789 −1.5147864 × 10⁻⁵ 2.263225 ×10⁻⁷ 0 19 0.0031378482  −0.00062506022 0 0

TABLE 9 Diffractive phase profile coefficients for diffractive surface1424 in system 1400. a₁r² coefficient a₂r⁴ coefficient a₃r⁶ coefficientSurface # (mm⁻²) (mm⁻⁴) (mm⁻⁶) 14 −322040.42 30853610 −3.483994 × 10⁹

TABLE 10 Prescription for objective 2102. Radius Thickness DiameterSurface # (mm) (mm) Material (mm) Comment 1 ∞ 97.951 92.86516 2 — 0 — 3∞ −97.951 95.92794 4 — 0 — 5 156.123 27.482 S-BSM15 129.776 Objective 6256.231 9.426 114.898 7 — 0 — 8 463.834 14 S-BSM15 109.12 9 80.073 18S-FPL51 92.502 10 ∞ 34.132 82.63025 11 ∞ 62.611 76 12 ∞ 18 S-FPL51101.68 13 −116.086 16.694 S-LAM60 104.204 14 −347.157 29.141 S-BSM15116.272 15 −175.677 250.924 128.044 16 ∞ −381.459 13.88646 17 — 381.459— — 18 ∞ 40 0 19 — 0 — — 20 ∞ 0 10.54326

TABLE 11 Prescription for microcamera 2110 (surfaces are numbered withinsystem 2100). Radius Thickness Diameter Surface # (mm) (mm) Material(mm) Comment 21 30.14496 3 E48R 10.2 Microcamera 22 ∞ 0 E48R 10.2 23−31.41865 3 OKP4 10.2 24 −66.98881 22.396 10.2 25 ∞ 0.5 S-BSL7 8.11323926 ∞ 1 8.085878 STO 200 3 E48R 7 28 −50 13 8.312635 Stop 29 ∞ 0 9.47886730 ∞ 0 9.478867 31 59.53304 3 OKP4 9.507213 32 ∞ 0 OKP4 9.679415 3319.10577 4 E48R 9.72629 34 ∞ 0 E48R 10.0808 35 −29.76652 4 10.04253 36 ∞0 10.17668 37 ∞ 0 10.17668 38 7.612243 10 E48R 10.23967 39 ∞ 0 E48R6.234178 40 4.229024 1.75 5.943628 41 ∞ 0 5.657099 42 ∞ 0 5.657099 43 ∞0.4 S-BSL7 5.657099 44 ∞ 0.1 5.591093 IMA ∞ 4.572603

TABLE 12a Prescription for system 2800 (based on materials availablefrom OHARA). Radius Thickness Diameter Surface # (mm) (mm) Material (mm)Comment 1 ∞ ∞ Object Surface 2 3048 3048 MIRROR 762 Objective Mirror 3 ∞∞ Intermediate Image Surface 4 79.96229 79.96229 S-BAH28 11 MicrocameraStart 5 −79.96229 −79.96229 11 6 15.57851 15.57851 S-LAL12 11 7−205.4075 −205.4075 S-TIH6 10.39214 8 26.35023 26.35023 9.312318 9 ∞ ∞4.450593 Stop 10 −6.060214 −6.060214 S-T1M27 6.008102 11 8.6837398.683739 S-BSM14 7.777471 12 −8.683739 −8.683739 8.626162 13 30.1684830.16848 S-LAL12 11.01385 Focusing Element 14 −30.16848 −30.1684811.14327 15 8.901399 8.901399 S-BAH28 10.77103 16 6.575486 6.5754866.566129 Microcamera End 17 ∞ ∞ S-BSL7 6.012425 Sensor Window 18 ∞ ∞6.044184 19 ∞ ∞ 4.4 Image

TABLE 12b Additional prescription information for system 2800. Surface #N_(d) V_(d) 1 2 3 4 1.723420 37.955602 5 6 1.677900 55.341195 7 1.80518125.425363 8 9 10 1.639799 34.466422 11 1.603112 60.641080 12 13 1.67790055.341195 14 15 1.723420 37.955602 16 17 1.516330 64.142022 18 19

1-15. (canceled)
 16. A multiscale telescopic imaging system comprising:an objective lens, the objective lens being operative for forming afirst image of a scene at a first image surface, and the objective lensincluding at least one reflective surface; and a plurality ofmicrocameras, each microcamera being operative for reducing themagnitude of a first aberration, the plurality of microcameras beingoperative for relaying a plurality of image portions of the first imageto form a plurality of sub-images, wherein the plurality of microcamerasis arranged in a first arrangement of sub-groups, each sub-groupcomprising at least one microcamera, and wherein the sub-groups arearranged in a second arrangement that includes open space between atleast two adjacent sub-groups.
 17. The system of claim 16, wherein theobjective lens comprises a Schmidt corrector plate.
 18. The system ofclaim 16, wherein at least one of the plurality of microcameras has atleast one controllable camera setting that is selected from the groupconsisting of focus, exposure, gain, magnification, and dynamic range.19. The system of claim 16, wherein the first aberration is selectedfrom the group consisting of spherical aberration, chromatic aberration,and spherochromatism.
 20. The system of claim 16 wherein the firstarrangement defines a hexagonal uniformly redundant array.
 21. Thesystem of claim 16 wherein the system has a field of view that is equalto or greater than 10 degrees, and wherein the system has resolutionequal to or less than 2 arcseconds.
 22. The system of claim 16 wherein afirst sub-group of the plurality thereof includes (1) a firstmicrocamera that relays a first image portion and (2) a secondmicrocamera that relays a second image portion, and wherein the firstimage portion and the second image portion at least partially overlap.23. The system of claim 16 further including a processor that isoperative for forming a composite image of the scene based on theplurality of sub-images.
 24. A multiscale telescopic imaging systemcomprising: an objective lens, the objective lens being operative forforming a first image of a scene at a first image surface; and aplurality of microcameras, the plurality of microcameras being operativefor relaying a plurality of image portions of the first image to form aplurality of sub-images, wherein the plurality of microcameras isarranged in a first arrangement of sub-groups, each sub-group comprisingat least one microcamera, and wherein the sub-groups are arranged in asecond arrangement that includes open space between at least twoadjacent sub-groups.
 25. The system of claim 24 wherein at least onemicrocamera of the plurality thereof is operative for reducing themagnitude of a first aberration in its respective relayed image portion.26. The system of claim 25, wherein the first aberration is selectedfrom the group consisting of spherical aberration, chromatic aberration,and spherochromatism.
 27. The system of claim 24, wherein the objectivelens comprises a Schmidt corrector plate.
 28. The system of claim 24,wherein at least one of the plurality of microcameras has at least onecontrollable camera setting that is selected from the group consistingof focus, exposure, gain, magnification, and dynamic range.
 29. Thesystem of claim 24 wherein at least one sub-group of the pluralitythereof is arranged in a hexagonal uniformly redundant array.
 30. Thesystem of claim 24 wherein the first arrangement defines a hexagonaluniformly redundant array.
 31. The system of claim 24 wherein theobjective lens includes at least one reflective surface.
 32. The systemof claim 24 wherein the objective lens includes a double-gaussrefractive lens.
 33. The system of claim 24 wherein the system has afield of view that is equal to or greater than 10 degrees, and whereinthe system has resolution equal to or less than 2 arcseconds.
 34. Thesystem of claim 24 wherein a first image portion of the pluralitythereof and a second image portion of the plurality thereof at leastpartially overlap.
 35. The system of claim 24 further including aprocessor that is operative for forming an image of the scene based onat least one sub-image of the plurality thereof.